Dark Energy Explained via the Hawking-Hartle Quantum Wave and the Topology of Cosmic Crystallography - Download this document for free, or read online. Document in PDF available to download.

The aim ofthe present paper is to explain and accurately calculate the missing darkenergy density of the cosmos by scaling the Planck scale and using themethodology of the relatively novel discipline of cosmic crystallography andHawking-Hartle quantum wave solution of Wheeler-DeWitt equation. Following thisroad we arrive at a modified version of Einstein’s energy mass relation E = mc2 which predicts a cosmological energy density in astonishing accord with theWMAP and supernova measurements and analysis. We develop non-constructivelywhat may be termed super symmetric Penrose fractal tiling and find that theisomorphic length of this tiling is equal to the self affinity radius of auniverse which resembles an 11 dimensional Hilbert cube or a fractal M-theorywith a Hausdorff dimension where.It then turns out that the correct maximal quantum relativity energy-mass equationfor intergalactic scales is a simple relativistic scaling, in the sense ofWeyl-Nottale, of Einstein’s classical equation, namely EQR = 1-21-moc2 = 0.0450849 mc2 and that this energy is the ordinarymeasurable energy density of the quantum particle. This means that almost 95.5%of the energy of the cosmos is dark energy which by quantum particle-waveduality is the absolute value of the energy of the quantum wave and isproportional to the square of the curvature of the curled dimension ofspacetime namely where and is Hardy’s probability of quantum entanglement. Because of thequantum wave collapse on measurement this energy cannot be measured using ourcurrent technologies. The same result is obtained by involving all the 17 Steinspaces corresponding to 17 types of the wallpaper groups as well as the 230-11=219 three dimensional crystallographic group whichgives the number of the first level of massless particle-like states inHeterotic string theory. All these diverse subjects find here a unified viewpoint leading to the same result regarding the missing dark energy of theuniverse, which turned out to by synonymous with the absolute value of theenergy of the Hawking-Hartle quantum wave solution of Wheeler-DeWitt equationwhile ordinary energy is the energy of the quantum particle into which theHawking-Hartle wave collapse at cosmic energy measurement. In other words it isin the very act of measurement which causes our inability to measure the -Darkenergy of the quantum wave- in any direct way. The only hope if any to detectdark energy and utilize itin nuclear reactors is future development of sophisticated quantum wave non-demolition measurement instruments.

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